The problem with vigilante "justice" is that the word justice means different things to different people. The mob that killed Joseph Smith probably thought they were doing a good and necessary thing, but Mormons would undoubtedly say otherwise.

The main problem with extrajudicial violence is that sometimes the vigilantes have a moral code that is inconsistent with that of the majority of humanity. One example I can give of this is the Ku Klux Klan in the US. I don't even know where to begin to link to about this since there's so much and I don't want to just link to wikipedia, but I'm sure you can find plenty on the KKK if you want to do a little research on your own. Obviously, we all know about the intimidation, beatings, and lynchings. You see a lot of people today railing against laws that prevent people from wearing masks in public as part of a group (because people want to maintain anonymity while protesting), but really those laws come directly from efforts to combat the anonymization practiced by hooded klansmen.

Even if a vigilante group's morals are more or less in line with humanity's general moral compass, mistakes can easily be made without an impartial trial and appeals process. I could link to dozens of cases of people on death row that were released after new evidence came about, but you've heard about these types of cases before, so what's the point, right? And what about all the people brought to trial that were later found to be innocent? In all of those cases, that innocent person would have been punished/killed by vigilantes before the evidence exonerating them could be discovered/presented.

Here are some problem cases (since there are obviously so many, I'm just going to make you aware of some of them and let you ask for more information about anything specific):

• The Great Hanging at Gainesville, where many people were hanged in the southern US during the Civil War just for being Union sympathizers

• The Montana Vigilantes killed a bunch of purported criminals, but the last person they hanged did nothing more than express a concern that some of the others might have been innocent

• As I said earlier, many actions by the KKK

• The Sea Shepherds cause a lot of international problems

• The Thammasat University Massacre was perpetrated by vigilantes

• The IRA has committed many acts of vigilante violence that caused tension and retaliations by both the English and Irish governments.

• Sombra Negra tries to fight the corrupting influence of drug cartels, but is itself the remnant of former death squads, and committed some pretty terrible acts

Edit: The real problem with going back very far in history with this, however, is what exactly is a vigilante? The actions taken by budding Nazis in their rise to power was vigilantism, but once they were in power it was state-sanctioned so it's not vigilantism anymore. When private citizens in ancient Rome raised their own armies, was that vigilantism? When you live in a society without a judicial system, any action of violence could be classified as vigilantism, depending on how you wanted to define things. Terrorism seems to fit the definition that many apply to vigilantism. At what point, specifically, did the actions of the Taliban switch from being state-sanctioned to being vigilantism?